n-widths of Sobolev spaces in \(L^ p\)
type: Item
instance of: scholarly article
title: n-widths of Sobolev spaces in \(L^ p\)
zbMATH Open document ID: 0582.41018
DOI: 10.1007/BF01890021
author: Allan Pinkus
published in: Constructive Approximation
publication date: 1985-01-01T00:00:00Z
review text: Let \(W_ p^{(r)}=\{f: f\in C^{r-1}[0,1]\), \(f^{(r-1)}\) abs. cont., \(\| f^{(r)}\|_ p<\infty \}\), and set \(B_ p^{(r)}=\{f: f\in W_ p^{(r)}\), \(\| f^{(r)}\|_ p\leq 1\}\). We find the exact Kolmogorov, Gel'fand, linear, and Bernstein n-widths of \(B_ p^{(r)}\) in \(L^ p\) for all \(p\in (1,\infty)\). For the Kolmogorov n-width we show that for \(n\geq r\) there exists an optimal subspace of splines of degree r-1 with n-r fixed simple knots depending on p.
Mathematics Subject Classification ID: 41A45
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 3931653
zbMATH Keywords: Gel'fand n-widths
zbMATH Keywords: Bernstein n-widths
zbMATH Keywords: Kolmogorov n-width
MaRDI profile type: Publication
cites work: Q3261425
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cites work: Spline spaces are optimal for \(L^2\) n-width
cites work: On n-Widths in L ∞
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description: scientific article; zbMATH DE number 3931653